Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9913)

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`=-3/2

http://functions.wolfram.com/07.22.03.9913.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(3/2), 23/4}, -z] == (209 (Sqrt[Pi] (-3778256272415625 - 1450850408607600 z - 401967212774400 z^2 - 126107360870400 z^3 - 77604529766400 z^4 + 137963608473600 z^5 - 58864472948736 z^6 + 44849122246656 z^7 + 4599909974016 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (-1259418757471875 + 92117486260800 z - 5955069818880 z^2 - 8879354265600 z^3 + 9865468182528 z^4 - 4097587544064 z^5 + 2750926553088 z^6 + 286689067008 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (3778256272415625 - 2579289615302400 z - 122078931287040 z^2 - 24143631482880 z^3 + 15192421171200 z^4 - 5387348606976 z^5 + 2549398634496 z^6 + 283467841536 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(39899077948735488 z^(19/4))

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]