Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a83b)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=-3/2

http://functions.wolfram.com/07.22.03.a83b.01

Input Form

HypergeometricPFQ[{-(15/4)}, {-(3/2), 21/4}, -z] == (221 (Sqrt[Pi] (15346656950625 + 6569806320000 z + 2151515520000 z^2 + 917979955200 z^3 + 1669054464000 z^4 - 1017328435200 z^5 + 387553689600 z^6 + 161061273600 z^7 + 4294967296 z^8) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((-(-15346656950625 + 9799961094000 z + 698876640000 z^2 + 62376652800 z^3 - 57988546560 z^4 + 15775825920 z^5 + 9814671360 z^6 + 268435456 z^7)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (5115552316875 - 148602762000 z + 94004064000 z^2 + 108928512000 z^3 - 64677150720 z^4 + 22444769280 z^5 + 10015997952 z^6 + 268435456 z^7) Sin[2 Sqrt[z]])))/ (461794883665920 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]