Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8xy)

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

For fixed z and a₁=-11/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.a8xy.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(5/2), 21/4}, z] == (221 (-4 z^(1/4) (5524796502225 + 7366395336300 Sqrt[z] + 4130218239840 z + 1016964305280 z^(3/2) + 25027833600 z^2 + 14763893760 z^(5/2) + 11183800320 z^3 - 32836091904 z^(7/2) + 2514419712 z^4 - 9110814720 z^(9/2) + 257949696 z^5 - 981467136 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (5524796502225 - 7366395336300 Sqrt[z] + 4130218239840 z - 1016964305280 z^(3/2) + 25027833600 z^2 - 14763893760 z^(5/2) + 11183800320 z^3 + 32836091904 z^(7/2) + 2514419712 z^4 + 9110814720 z^(9/2) + 257949696 z^5 + 981467136 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (5524796502225 - 1762898029200 z + 408787948800 z^2 - 114747494400 z^3 + 122397327360 z^4 + 35606495232 z^5 + 3875536896 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (5524796502225 - 1762898029200 z + 408787948800 z^2 - 114747494400 z^3 + 122397327360 z^4 + 35606495232 z^5 + 3875536896 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/(115448720916480 z^(17/4))

Standard Form

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MathML Form

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Rule Form

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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]