Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7td)

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`=7/2

http://functions.wolfram.com/07.22.03.a7td.01

Input Form

HypergeometricPFQ[{-(17/4)}, {7/2, -(1/4)}, -z] == (1/(261654624 z^(5/2))) (-2 Sqrt[z] (20675655 + 20049120 z - 39460608 z^2 + 357875712 z^3 + 104370432 z^4 + 5627904 z^5 + 65536 z^6) Cos[2 Sqrt[z]] - 64 Sqrt[Pi] z^(15/4) (23468211 + 6587568 z + 352512 z^2 + 4096 z^3) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - (-20675655 + 7518420 z - 57283200 z^2 + 147667968 z^3 + 50177664 z^4 + 2789376 z^5 + 32768 z^6) 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]