Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8394)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8394.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, -(7/4)}, z] == (1/(1343090548800 z^(5/2))) ((-135528918525 + 135528918525 E^(4 Sqrt[z]) - 271057837050 Sqrt[z] - 271057837050 E^(4 Sqrt[z]) Sqrt[z] - 95667471900 z + 95667471900 E^(4 Sqrt[z]) z + 170075505600 z^(3/2) + 170075505600 E^(4 Sqrt[z]) z^(3/2) - 130827312000 z^2 + 130827312000 E^(4 Sqrt[z]) z^2 + 86747189760 z^(5/2) + 86747189760 E^(4 Sqrt[z]) z^(5/2) - 59087508480 z^3 + 59087508480 E^(4 Sqrt[z]) z^3 + 46081474560 z^(7/2) + 46081474560 E^(4 Sqrt[z]) z^(7/2) - 46130135040 z^4 + 46130135040 E^(4 Sqrt[z]) z^4 + 71693107200 z^(9/2) + 71693107200 E^(4 Sqrt[z]) z^(9/2) - 313944440832 z^5 + 313944440832 E^(4 Sqrt[z]) z^5 - 10005848064 z^(11/2) - 10005848064 E^(4 Sqrt[z]) z^(11/2) + 40891219968 z^6 - 40891219968 E^(4 Sqrt[z]) z^6 + 296484864 z^(13/2) + 296484864 E^(4 Sqrt[z]) z^(13/2) - 1192230912 z^7 + 1192230912 E^(4 Sqrt[z]) z^7 - 2097152 z^(15/2) - 2097152 E^(4 Sqrt[z]) z^(15/2) + 8388608 z^8 - 8388608 E^(4 Sqrt[z]) z^8 + 2048 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-156828375 + 20074032 z - 582912 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 2048 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-156828375 + 20074032 z - 582912 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<mrow> <mn> 46130135040 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 46081474560 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 46081474560 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 59087508480 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 59087508480 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 86747189760 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z 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⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 95667471900 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 271057837050 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 271057837050 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 135528918525 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> - </mo> <mn> 135528918525 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 23 <sep /> 4 </cn> </apply> </list> 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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]