Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7735)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-17/4

http://functions.wolfram.com/07.22.03.7735.01

Input Form

HypergeometricPFQ[{6}, {-(17/4), 5/4}, -z] == (1/(76377600 z^(1/4))) (-2 z^(1/4) (24025275 + 37977840 z - 28080 z^2 - 1518080 z^3 + 192512 z^4) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] ((62214075 - 18433800 z - 112107600 z^2 - 29731200 z^3 - 5447680 z^4 + 32768 z^5) Cos[2 Sqrt[z]] + 190 Sqrt[z] (654885 + 679140 z - 41712 z^2 - 38400 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-190 Sqrt[z] (654885 + 679140 z - 41712 z^2 - 38400 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + (62214075 - 18433800 z - 112107600 z^2 - 29731200 z^3 - 5447680 z^4 + 32768 z^5) Sin[2 Sqrt[z]]))

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]