Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8370)

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`=5/2

http://functions.wolfram.com/07.22.03.8370.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, 17/4}, z] == (-4 z^(1/4) (-30951416768146875 - 41268555690862500 Sqrt[z] + 132059378210760000 z - 676733890623436800 z^(3/2) + 524710042195046400 z^2 - 3470381795510784000 z^(5/2) - 758934524668723200 z^3 + 3403019645190144000 z^(7/2) + 146521354585374720 z^4 - 610132901387304960 z^(9/2) - 8616821863219200 z^5 + 35020728466145280 z^(11/2) + 189861042585600 z^6 - 764222053023744 z^(13/2) - 1607391510528 z^7 + 6442450944000 z^(15/2) + 4294967296 z^8 - 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-30951416768146875 + 41268555690862500 Sqrt[z] + 132059378210760000 z + 676733890623436800 z^(3/2) + 524710042195046400 z^2 + 3470381795510784000 z^(5/2) - 758934524668723200 z^3 - 3403019645190144000 z^(7/2) + 146521354585374720 z^4 + 610132901387304960 z^(9/2) - 8616821863219200 z^5 - 35020728466145280 z^(11/2) + 189861042585600 z^6 + 764222053023744 z^(13/2) - 1607391510528 z^7 - 6442450944000 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-30951416768146875 + 165074222763450000 z + 2112950051372160000 z^2 + 15776693716912128000 z^3 - 14023727748366336000 z^4 + 2465710373339136000 z^5 - 140646581010432000 z^6 + 3061694280499200 z^7 - 25782688677888 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (-30951416768146875 + 165074222763450000 z + 2112950051372160000 z^2 + 15776693716912128000 z^3 - 14023727748366336000 z^4 + 2465710373339136000 z^5 - 140646581010432000 z^6 + 3061694280499200 z^7 - 25782688677888 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(67232284180217856000 z^(13/4))

Standard Form

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MathML Form

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<mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <msup> <mi> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 68719476736 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 9 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 25782688677888 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 8 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3061694280499200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 7 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 140646581010432000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 6 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2465710373339136000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 5 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14023727748366336000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 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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]