Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7903)

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=5/4

http://functions.wolfram.com/07.22.03.7903.01

Input Form

HypergeometricPFQ[{6}, {5/4, 23/4}, -z] == (1/(268435456 z^(19/4))) (4389 (4 z^(3/4) (121275 - 46200 z + 9600 z^2 - 2048 z^3) + Sqrt[Pi] FresnelC[(2 z^(1/4))/Sqrt[Pi]] (2 Sqrt[z] (-363825 + 277200 z - 77280 z^2 + 15360 z^3 + 8192 z^4) Cos[2 Sqrt[z]] + 5 (72765 - 152460 z + 63504 z^2 - 13824 z^3 + 4096 z^4) Sin[2 Sqrt[z]]) + Sqrt[Pi] FresnelS[(2 z^(1/4))/Sqrt[Pi]] (-5 (72765 - 152460 z + 63504 z^2 - 13824 z^3 + 4096 z^4) Cos[2 Sqrt[z]] + 2 Sqrt[z] (-363825 + 277200 z - 77280 z^2 + 15360 z^3 + 8192 z^4) 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]