Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7us)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a7us.01

Input Form

HypergeometricPFQ[{-(17/4)}, {9/2, 3/4}, z] == (1/(9270049536 z^(7/2))) ((103378275 - 103378275 E^(4 Sqrt[z]) + 206756550 Sqrt[z] + 206756550 E^(4 Sqrt[z]) Sqrt[z] + 90221040 z - 90221040 E^(4 Sqrt[z]) z - 95233320 z^(3/2) - 95233320 E^(4 Sqrt[z]) z^(3/2) - 14320800 z^2 + 14320800 E^(4 Sqrt[z]) z^2 + 171849600 z^(5/2) + 171849600 E^(4 Sqrt[z]) z^(5/2) - 534643200 z^3 + 534643200 E^(4 Sqrt[z]) z^3 + 3274739712 z^(7/2) + 3274739712 E^(4 Sqrt[z]) z^(7/2) + 553479804 z^4 - 553479804 E^(4 Sqrt[z]) z^4 - 2400677040 z^(9/2) - 2400677040 E^(4 Sqrt[z]) z^(9/2) - 69067968 z^5 + 69067968 E^(4 Sqrt[z]) z^5 + 282532608 z^(11/2) + 282532608 E^(4 Sqrt[z]) z^(11/2) + 2143232 z^6 - 2143232 E^(4 Sqrt[z]) z^6 - 8622080 z^(13/2) - 8622080 E^(4 Sqrt[z]) z^(13/2) - 16384 z^7 + 16384 E^(4 Sqrt[z]) z^7 + 65536 z^(15/2) + 65536 E^(4 Sqrt[z]) z^(15/2) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (3637572705 - 2450575296 z + 284124672 z^2 - 8634368 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (-3637572705 + 2450575296 z - 284124672 z^2 + 8634368 z^3 - 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/ E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<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> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 14320800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 95233320 </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> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 95233320 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 90221040 </mn> <mo> ⁢ </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> 90221040 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 206756550 </mn> <mo> ⁢ </mo> <msup> <mi> 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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]