Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8507)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.8507.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 9/4}, -z] == (Sqrt[Pi] z^(13/4) (-19619612216906625 + 129258621664326000 z + 98482759363296000 z^2 + 15006896664883200 z^3 + 752697011404800 z^4 + 14597760221184 z^5 + 110746402816 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-1153896891840000 - 732632947200000 z - 1375396252876800 z^2 + 4615289458250625 z^3 + 5422837959776160 z^4 + 896976055422720 z^5 + 46213222809600 z^6 + 905932898304 z^7 + 6905921536 z^8 + 16777216 z^9) Cos[2 Sqrt[z]] + 4 (-144237111480000 + 100737030240000 z + 1465265894400 z^2 - 1594209293107200 z^3 + 7214091789799125 z^4 + 5996493786618720 z^5 + 929467536480000 z^6 + 46875292090368 z^7 + 911069085696 z^8 + 6918504448 z^9 + 16777216 z^10) Sin[2 Sqrt[z]]))/ (132467784332083200 z^(9/2))

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]